Direct discovery · Mathematics

Astra strengthens an asymptotic lower bound on large gaps between primes

A stronger asymptotic lower bound for the largest consecutive-prime gap below X, accompanied by a public Lean formalization.

Summary

OpenAI released a paper and Lean development proving G(X) is bounded below by a constant times log X (log log X)^2 log₄ X / (log₃ X)^2 for sufficiently large X. The repository provides the formal statement and comparator instructions.

AI role

GPT-6 Astra produced the argument using weighted short translates to construct prime-free intervals.

Narrative role

This adds an asymptotic improvement alongside the separate short-gap result, extending AI-attributed mathematics beyond finite numerical optimization.

Caveat

The bound is asymptotic and does not settle the optimal growth of prime gaps. Formalization is supplied by the authors; this run inspected the artifact and instructions but did not rebuild it or establish independent expert acceptance.